Deciphering All Those Minimum Aberration Criteria for Experimental Designs

ABSTRACT

The minimum aberration is an efficient criterion to evaluate fractional factorial designs. The concept of minimum aberration was first proposed by Fries and Hunter (1980) for regular two-level designs. Since then, increasing numbers of statisticians and quality engineers have been involved in extending minimum aberration criterion into wider applications such as two-level nonregular, multilevel, and mixed-level fractional-factorial designs. In the past decade, many minimum aberration criteria definitions have been developed. However, those useful criteria have not been widely recognized and used by practitioners for the real-world problems. Via examples, this article comprehensively reviews the minimum aberration criteria definitions regarding their advantages, limitations, drawbacks, and relationships.

KEYWORDS:

• experimental designs
• minimum aberration criterion
• mixed-level designs
• multilevel designs
• nonregular designs

Notes

A ₁(d ₃) (0² + 0² + 0² + 0² + 0² + 0²)/12² = 0.

A ₂(d ₃) (0² + 0² + 0² + 0² + 0² + 0² + 0² + 0² + 1.9994² + 0² + 0² + 0² + 0² + 3.9988²)/12² = 0.1388.